1 | initial version |

1) Yes,

```
sage: L = lie_algebras.sp(QQ,4)
sage: L
Lie algebra of ['C', 2] in the Chevalley basis
```

If you want a basis try `L.basis()`

2) you can get this directly from the Cartan Matrix which by definition will get you `2`

since `h(1)=alphacheck[1]`

is the coroot associated to `alpha[1]`

. In this particular case you could try

```
sage: L = lie_algebras.sp(QQ,4, representation='matrix')
sage: L.simple_root(1,L.h(1))
2
```

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